For future reference, the seat reservation for a seat with oversized baggage on the Nishi Kyushu Shinkansen came for free with my JR Kyushu rail pass. And the station attendant was very pleased that I bothered to ask for one (apparently many people don't). In the event, my bag fit into the regular baggage racks on the Shinkansen as well as the other JR Kyushu trains without problems.